The rewrite relation of the following TRS is considered.
U11(tt,M,N) | → | U12(tt,activate(M),activate(N)) | (1) |
U12(tt,M,N) | → | s(plus(activate(N),activate(M))) | (2) |
U21(tt,M,N) | → | U22(tt,activate(M),activate(N)) | (3) |
U22(tt,M,N) | → | plus(x(activate(N),activate(M)),activate(N)) | (4) |
plus(N,0) | → | N | (5) |
plus(N,s(M)) | → | U11(tt,M,N) | (6) |
x(N,0) | → | 0 | (7) |
x(N,s(M)) | → | U21(tt,M,N) | (8) |
activate(X) | → | X | (9) |
U12#(tt,M,N) | → | activate#(N) | (10) |
U21#(tt,M,N) | → | activate#(M) | (11) |
U22#(tt,M,N) | → | x#(activate(N),activate(M)) | (12) |
U11#(tt,M,N) | → | activate#(M) | (13) |
x#(N,s(M)) | → | U21#(tt,M,N) | (14) |
U22#(tt,M,N) | → | plus#(x(activate(N),activate(M)),activate(N)) | (15) |
U22#(tt,M,N) | → | activate#(N) | (16) |
U21#(tt,M,N) | → | activate#(N) | (17) |
U11#(tt,M,N) | → | activate#(N) | (18) |
U21#(tt,M,N) | → | U22#(tt,activate(M),activate(N)) | (19) |
U22#(tt,M,N) | → | activate#(N) | (16) |
U12#(tt,M,N) | → | activate#(M) | (20) |
U12#(tt,M,N) | → | plus#(activate(N),activate(M)) | (21) |
U11#(tt,M,N) | → | U12#(tt,activate(M),activate(N)) | (22) |
U22#(tt,M,N) | → | activate#(M) | (23) |
plus#(N,s(M)) | → | U11#(tt,M,N) | (24) |
The dependency pairs are split into 2 components.
x#(N,s(M)) | → | U21#(tt,M,N) | (14) |
U22#(tt,M,N) | → | x#(activate(N),activate(M)) | (12) |
U21#(tt,M,N) | → | U22#(tt,activate(M),activate(N)) | (19) |
[U21(x1, x2, x3)] | = | 0 |
[U11(x1, x2, x3)] | = | 0 |
[s(x1)] | = | x1 + 7 |
[activate(x1)] | = | x1 + 1 |
[plus#(x1, x2)] | = | 0 |
[activate#(x1)] | = | 0 |
[U12(x1, x2, x3)] | = | 0 |
[x(x1, x2)] | = | 0 |
[U12#(x1, x2, x3)] | = | 0 |
[0] | = | 0 |
[x#(x1, x2)] | = | x1 + x2 + 0 |
[plus(x1, x2)] | = | 0 |
[U11#(x1, x2, x3)] | = | 0 |
[U21#(x1, x2, x3)] | = | x1 + x2 + x3 + 4 |
[U22#(x1, x2, x3)] | = | x1 + x2 + x3 + 1 |
[tt] | = | 2 |
[U22(x1, x2, x3)] | = | 0 |
activate(X) | → | X | (9) |
x#(N,s(M)) | → | U21#(tt,M,N) | (14) |
U22#(tt,M,N) | → | x#(activate(N),activate(M)) | (12) |
U21#(tt,M,N) | → | U22#(tt,activate(M),activate(N)) | (19) |
The dependency pairs are split into 0 components.
plus#(N,s(M)) | → | U11#(tt,M,N) | (24) |
U11#(tt,M,N) | → | U12#(tt,activate(M),activate(N)) | (22) |
U12#(tt,M,N) | → | plus#(activate(N),activate(M)) | (21) |
[U21(x1, x2, x3)] | = | 0 |
[U11(x1, x2, x3)] | = | 0 |
[s(x1)] | = | x1 + 7 |
[activate(x1)] | = | x1 + 1 |
[plus#(x1, x2)] | = | x1 + x2 + 0 |
[activate#(x1)] | = | 0 |
[U12(x1, x2, x3)] | = | 0 |
[x(x1, x2)] | = | 0 |
[U12#(x1, x2, x3)] | = | x1 + x2 + x3 + 0 |
[0] | = | 0 |
[x#(x1, x2)] | = | x1 + x2 + 0 |
[plus(x1, x2)] | = | 0 |
[U11#(x1, x2, x3)] | = | x1 + x2 + x3 + 3 |
[U21#(x1, x2, x3)] | = | 4 |
[U22#(x1, x2, x3)] | = | x2 + x3 + 1 |
[tt] | = | 3 |
[U22(x1, x2, x3)] | = | 0 |
activate(X) | → | X | (9) |
plus#(N,s(M)) | → | U11#(tt,M,N) | (24) |
U11#(tt,M,N) | → | U12#(tt,activate(M),activate(N)) | (22) |
U12#(tt,M,N) | → | plus#(activate(N),activate(M)) | (21) |
The dependency pairs are split into 0 components.